Orbits and characters associated to highest weight representations

Collingwood, David H.

doi:10.1090/S0002-9939-1992-1074750-6

Orbits and characters associated to highest weight representations
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by David H. Collingwood PDF

Proc. Amer. Math. Soc. 114 (1992), 1157-1165 Request permission

Abstract:

We relate two different orbit decompositions of the flag variety. This allows us to pass from the closed formulas of Boe, Enright, and Shelton for the formal character of an irreducible highest weight representation to closed formulas for the distributional character written as a sum of characters of generalized principal series representations. Otherwise put, we give a dictionary between certain Lusztig-Vogan polynomials arising in Harish-Chandra module theory and the Kazhdan-Lusztig polynomials associated to a relative category $\mathcal {O}$ of Hermitian symmetric type.

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